Conventionally, there has been known a high expansion ratio cycle engine equipped with a supercharger in which an expansion ratio is set greater than a compression ratio. Such a high expansion ratio cycle engine can be equipped with a variable valve timing mechanism capable of changing opening timing of an exhaust valve. Then, when it is determined that the high expansion ratio cycle engine is operated at a low and/or middle speed range and a low load range, and becomes transient timing of acceleration, the high expansion ratio engine activates the variable valve timing mechanism so as to advance the opening timing of the exhaust valve, thereby preventing degradation of the response of the supercharger (see Patent Document 1).